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IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 16, NO. 3, MAY 2001 351

Digital Scalar Pulse-Width Modulation: A SimpleApproach to Introduce Non-Sinusoidal Modulating

WaveformsCursino Brando Jacobina, Senior Member, IEEE, Antonio Marcus Nogueira Lima, Member, IEEE,

Edison Roberto Cabral da Silva, Senior Member, IEEE, Raimundo Nazareno Cunha Alves, and Paulo Fernando Seixas

AbstractThe digital scalar pulse-width modulation (DSPWM)gathers the characteristics of simplicity of implementation foundin the regular sampling with the flexibility of manipulation ofthe switching patterns in the space vector modulation (SVPWM).This paper establishes a correlation between the SVPWM andDSPWM techniques. It also shows how to make the DSPWMstrategy equivalent to the SVPWM technique without loosing itssimplicity of implementation. By using such equivalence concept amicroprocessor-based scheme, which uses standard timer circuitsand a simple software algorithm, is proposed to implement

the DSPWM technique. The introduction of the distributionratio in this technique, allows the development of a systematicapproach for implementing of either conventional or any modifiedvector strategies without changing the modulator scheme. Thiscorresponds to generate any attractive nonsinusoidal modulatingsignals (NSMS) in the carrier-based modulation techniques.Furthermore, the simple digital blocks can be easily implementedas an specialized integrated circuit. Simulated and experimentalresults demonstrate the validity of the proposed methods.

Index TermsPulse-width modulation, three-phase inverter.

I. INTRODUCTION

THE classical sine-triangle modulation, or natural sam-

pling modulation (NSPWM), compares a high frequencytriangular carrier with three reference signals, known as mod-

ulating signals, to create gating pulses for the switches of the

power converter [1]. This technique is basically an analog

domain technique and its digital version led to the tech-

nique named as regular-sampled PWM (RSPWM) [2]. In the

RSPWM technique, the modulating signal is sampled at each

period (symmetric regular sampling) or at every peak (asym-

metric regular sampling) of the triangular signal to produce

a sampled-hold modulating wave. Its digital comparison to a

triangular signal, generated by up-down counters, define the

switching instants. In other words, the corresponding time in-

tervals are computed in real time from the respective sampledvalue [3]. Differently from the previous methods, the space

vector pulse-width modulation (SVPWM) technique [4], [5]

does not consider each of the three phases as a separate entity.

The three-phase voltages are simultaneously performed within

Manuscript received September 1, 1998; revised January 4, 2001. Recom-mended by Associate Editor F. D. Tan.

The authors are with the Departamento de Engenharia Eltrica, Universi-dade Federal da Paraba, Campina Grande, Paraiba 58109-970, Brazil (e-mail:[email protected]).

Publisher Item Identifier S 0885-8993(01)04026-1.

a two-dimensional reference frame ( plane), the complex ref-

erence voltage vector being processed as a whole. Because its

flexibility of manipulation, the SVPWM technique is widely

employed, nowadays [3].

It is well-known that the addition of proper zero-sequence

components to the modulating signals generates nonsinusoidal

modulating signals (NSMS). Several different waveform pro-

files can be used as modulating signals [3], [6]. These NSMS

improve the performance of both NSPWM and RSPWM [7],[8]. On the other hand, the same effect obtained by the use

of NSMS in carrier-based techniques, is achieved with both

conventional SVPWM and modified SVPWM techniques. It

should be noted that the modified SVPWM strategy is known

in the literature under names such as two-phase modulation

[9], bus-clamping modulation [10], or discontinuous modu-

lation [11].

Several authors have discussed the correlation among the

NSPWM, RSPWM, and SVPWM techniques, under different

focuses. With that purpose, the concept of ordering of the ref-

erence voltages has been used to establish the analogy among

the sectors defined by the active vectors and the segments of

60 , existing in a period of the references. Also, the concept

of distribution ratio [12], named as apportioning factor in

[8] and defined as the relation between the time of application

of one of the two null vectors and the total null-vector time,

has been employed. In fact, properly choosing the distribution

factor determines both the distribution of the zero voltage

vectors inside the sampling period and its correspondence to

the modified SVPWM [8], [12][14].

The alternative digital scalar pulse-width modulation

(DSPWM) technique imposes, to the pole voltage of an inverter

leg, an average value that corresponds to each reference phase

within the sampling interval [15]. Such strategy is of simpler

implementation than the SVPWM technique, reducing theeffort of calculation [16]. The technique introduced in [17] has

a similar treatment by using the concept of reallocation of the

effective time. This effective time is in fact the sum of the

times of application of the active vectors. The pulse-widths are

ordered and the sum of times is appropriately moved within the

sampling period.

Different methods have been employed to implement the re-

sultant modulators of these recent studies. In [17], an algorithm

is provided and implemented with a DSP TMS320C31. How-

ever, because of the correspondence between of the carrier-

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356 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 16, NO. 3, MAY 2001

Fig. 9. Simulation results for . (a) Free-wheeling time

intervals. (b) Load current. (c) Voltage

.

e) calculating the modified time intervals ,

and ;

f) programming the three timers associated with each phase

with values , and .

It can be noted that the technique of reversing the pattern in

the next sampling interval can also be used. In this case the cal-

culated values of and are valid for the first sampling in-

terval. In the second interval, to achieve the reversing, the cal-

culated values of and are interchanged as illustrated in

Figs. 3 and 4.

Fig. 10. Simulation results when one phase is clamped for . (a) Free-

wheeling time intervals. (b) Load current. (c) Voltage

.

VI. HARDWAREIMPLEMENTATION

The hardware implementation of the idea outlined in Sec-

tions III and IV, consists in synthesizing the zero-sequence com-

ponent, , to be added to the three-phase reference signals.

From (24), (25), (28), (29), and (11), it comes

(30)

where and are the maximum and the minimum values,

respectively.

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358 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 16, NO. 3, MAY 2001

Fig. 13. Experimental results when one phase is clamped for .(a) Machine current. (b) Voltage .

depth was . In the case of Figs. 10 and 11 the switching fre-quency was increased by to make the power devices switch

as fast as in the case of Fig. 9. For comparison purposes, the load

current presented in these figures are superimposed to the ideal

current waveforms (inner curve). The ideal waveforms were ob-

tained by assuming the machine as supplied by a sinusoidal

three-phase source. Note that the DSPWM imposes correctly

the desired free-wheeling time intervals. One can observe by

comparing the results of Figs. 9 and 10 that the current ripple

has a minimum for , as expected for such modulation

depth.

VIII. EXPERIMENTAL RESULTS

Fig. 12 presents the machine voltage waveform obtained ex-

perimentally when an AC drive is used. The ac drive consists

of a Pentiummicrocomputer equipped with a plug-in board, a

three-phase six-switch (IGBT) inverter and a three-phase induc-

tion motor ( , , ,

mH, mH and H). A programmable timer

unit in the plug-in board generate the command signal to switch

on and off the power switches.

Figs. 1214 show and withthe real-time implementa-

tion of the DSPWM algorithm. Fig. 12 corresponds to the case

where and s. Fig. 13 corresponds to the case

when one phase is clamped for and s. For the

Fig. 14. Experimental results when one phase is clamped for .(a) Machine current. (b) Voltage .

results presented in Figs. 12 and 13, the modulation depth was. For Fig. 14, the modulation depth was . One can

also observe by comparing the experimental results of Figs. 12

and 13 that the current ripple has a minimum for , as ex-

pected for such modulation depth.

IX. CONCLUSIONS

This paper shows that it is possible to obtain the same results

as those obtained with the space vector modulation by using

a digital scalar modulation approach. Such equivalence was

employed to propose a simple software algorithm to generate

the space vector modulation from the scalar implementation.

A simple hardware version of the proposed scheme was alsopresented. The proposed scheme provides a direct method to

deal with nonsinusoidal modulating waveforms. The proposed

scheme was evaluated mathematically and tested via computer

simulations and experimental tests.

REFERENCES

[1] A. Schnung and H. Stemmler, Static frequency changers with subhar-monic control in conjunction with reversible variable speed ac drives,

Brown Boveri Rev., pp. 555577, 1964.[2] S. R. Bowes, New sinusoidal pulsewidth-modulated invertor, Proc.

Inst. Elect. Eng., vol. 122, pp. 12791285, Nov. 1975.[3] J. Holtz, Pulsewidth modulation for electronic power conversion,

Proc. IEEE, vol. 82, pp. 11941214, Aug. 1994.

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JACOBINAet al.: DIGITAL SCALAR PULSE-WIDTH MODULATION 359

[4] G. Pfaff, A. Weschta, and A. F. Wick, Design and experimental resultsof a brushless ac servo drive, IEEE Trans. Ind. Applicat., vol. 20, pp.814821, Jul./Aug. 1984.

[5] H. W. Van der Broeck, H.-C. Skudelny, and G. V. Stanke, Analysis andrealization of a pulsewidth modulator based on voltage space vectors,

IEEE Trans. Ind. Applicat., vol. 24, pp. 142150, Jan./Feb. 1988.[6] L. Abraham and R. Blumel, Optimization of three phase pattern by

variable zero sequence component, in Proc. Conf. Rec. EPE, 1991, pp.169174.

[7] M. Depenbrock, Pulse-width control of a 3-phase inverter with nonsi-nusoidal phase voltages, in Proc. Conf. Rec. IAS, 1977, pp. 399403.[8] J. Sun and H. Grotstollen, Optimized space vector modulation and reg-

ular-sampled pwm: A reexamination, in Proc. Conf. Rec. IAS, 1996,pp. 956963.

[9] L. Abraham and R. Blumel, Optimization of three phase pulse patternby variable zero sequence component, in Proc. Conf. Rec. EPE, 1991,pp. 272277.

[10] P. G. Handley and J. T. Boys, Practical real-time pwm modulators: Anassessment,Proc. Inst. Elect. Eng. B, vol. 139, pp. 96102, Mar. 1992.

[11] H. W. van der Broeck, Analysis of the harmonics in voltage fed in-verter drives caused by pwm schemes with discontinuous switching op-eration, inProc. Conf. Rec. EPE, 1991, pp. 32613266.

[12] R. N. C. Alves, A. M. N. Lima, E. R. C. da Silva, and C. B. Jacobina, Anew approach to the problem of synthezising nonsinusoidal waveformsfor analog and digital implementations of space vector pwm strategies,inProc. Conf. Rec. COBEP-Brazil, 1991, pp. 228233.

[13] V. Blasko, A hybrid pwm strategy combining modified space vectorand triangle comparison methods, in Proc. Conf. Rec. PESC, 1996, pp.18721878.

[14] D. G. Holmes, The significance of zero space vector placement for car-rier based pwmschemes, in Proc. Conf. Rec. IAS, 1995, pp. 24512458.

[15] C. B. Jacobina, E. R. C. da Silva, A. M. N. Lima, and R. L. A. Ribeiro,Vector andscalar control of a four switchthree phase inverter, in Proc.Conf. Rec. IAS, 1995, pp. 24222429.

[16] C.B. Jacobina, A.M. N.Lima, and E.R. C.da Silva, Pwmspace vectorbased on digital scalarmodulation, in Proc. Conf. Rec. PESC, 1997,pp.100105.

[17] D. W. Chung, J. S. Kim, and S. K. Sul, Unified voltage modulationtechnique for real time three-phase power conversion, in Proc. Conf.

Rec. IAS, 1996, pp. 921926.[18] A. Haras and E. Roye, Vector pwm modulator with continuous

transition to the six-step mode., in Proc. Conf. Rec. EPE, 1995, pp.17291734.

[19] N. Pop and A. Kelemen, Pulse-width modulation with extended mod-ulation depth range for three-phase voltage converters, in Proc. Conf.Rec. EPE, 1995, pp. 17951800.

[20] P. F. Seixas, A. M. N. Lima, and G. S. Deep, Digital control of cur-rentsin permanent magnet synchronous motor (in Portuguese), in Proc.Conf. Rec. CBA-Brazil, 1990, pp. 980984.

[21] P. F. Seixas, Commande numrique dune machine synchrone autopi-lote, Ph.D. thesis, INPT, Toulouse, France, 1988.

Cursino Brando Jacobina (S78M78SM98)was born in Correntes, Pernambuco, Brazil, in 1955.He received the B.S. degree in electrical engineeringfrom the Federal University of Paraba, CampinaGrande, Brazil, in 1978 and the Diplme dEtudes

Approfondies and Ph.D. degrees from the InstitutNational Polytechnique de Toulouse, Toulouse,France, in 1980 and 1983, respectively.

Since 1978, he has been with the Electrical Engi-neering Department, Federal University of Paraba,where he is now Professor of electrical engineering.

His research interests include electrical drives, power electronics, control sys-tems, and system identification.

Antonio Marcus Nogueira Lima (S77M89)was born in Recife, Pernambuco, Brazil, in 1958.He received the B.S. and M.S. degrees in electricalengineering from the Federal University of Paraba,Campina Grande, Brazil, in 1982 and 1985, re-spectively, and the Ph.D. degree from the InstitutNational Polytechnique de Toulouse, Toulouse,France, in 1989.

He was with the Escola Tcnica Redentorista,

Campina Grande, from 1977 to 1982, and was aProject Engineer at Sul-Amrica Philips, Recife,from 1982 to 1983. Since September 1983, he has been with the ElectricalEngineering Department, Federal University of Paraba, where he is nowProfessor of electrical engineering. His research interests are in the fields ofelectrical machines and drives, power electronics, electronic instrumentation,control systems, and system identification.

Edison Roberto Cabral da Silva(SM95) was bornin Pelotas, Brazil, on December 2, 1942. He receivedthe B.C.E.E. degree from the Polytechnic School ofPernambuco, Recife, Brazil, in 1965, the M.S.E.E.degree from the University of Rio de Janeiro, Brazil,in 1968, and the D.Eng. degree from the UniversityPaul Sabatier, Toulouse, France, in 1972.

In 1967, he joined the staff of the ElectricalEngineering Department, Federal University ofParaiba, Brazil, where he is a Professor of electricalengineering and Director of the Research Laboratory

on Industrial Electronics and Machine Drives. In 1990, he was with COPPE,Federal University of Rio de Janeiro, and from 1990 to 1991, he was withWEMPEC, University of Wisconsin, Madison, as a Visiting Professor. Hiscurrent research work is in the area of power electronics and motor drives. Hewas the General Chairman of the 1984 Joint Brazilian and Latin-AmericanConference on Automatic Control, sponsored by the Automatic ControlBrazilian Society.

Dr. da Silva is currently a Member-at-Large of the Executive Board, IEEEIndustrial Applications Society.

Raimundo Nazareno Cunha Alves was bornin Belm, Par, Brazil, in 1954. He received the

B.S. degree from the Federal University of Par in1977, and the M.S. and Ph.D. degrees in electricalengineering from the Federal University of Paraba,Campina Grande, Brazil, in 1983 and 1998, respec-tively.

Since August 1980, he has been with the ElectricalEngineering Department, Federal University of Par,where he is now Professor of electrical engineering.His research interests include power electronics and

electrical drives.

Paulo Fernando Seixaswas born in Belo Horizonte,Minas Gerais, Brazil, in 1957. He received the B.S.and M.S. degrees in electrical engineering from theFederal University of Minas Gerais, Belo Horizonte,

in 1980 and 1983, respectively, and the Ph.D.degree from the Institut National Polytechnique deToulouse, Toulouse, France, in 1988.

He has been with the Electrical Engineering De-partment, Federal University of Minas Gerais, since1980, where he is currently a Professor of electricalengineering. His research interests are in the fields of

electrical machines and drives, power electronics, and digital signal processing.